Wednesday, October 14, 2015

math

Anders asked me a few math questions.

He asked what it's called when you multiply a number by itself. I said you say you "squared" the number. He then asked about square roots, and I explained that's when you start with the squared number and ask what you can multiply by itself to get that number. We talked about a few squares, and then he asked me what's the square root of 13?

I said something between 3 and 4, and we talked about how I knew that. And then we talked about what 3.5 squared would be. So to do that, I drew some pictures for him. I started off with just a single square, and then talked about what it would look like if the square was twice as wide and twice as tall, and we agreed it would have 4 squares. I numbered those and also numbered the sides. Then we talked about a square that was three times as wide and tall as the original one, and I again numbered those. Anders got the point, and this let me say that's why we talk about "squaring" a number.

Then I said, ok, what if the sides were three and a half times as wide and tall as the original? I drew a new diagram:

...and after numbering the 9 full-size squares, I asked what would happen if we put two of the "skinny squares" together, and Anders was down with those together being the size of one "regular" square. So, going through the six skinny squares, we got to 12. And then I asked what 3.5 squared is, pointing to the remaining bit that we hadn't yet counted. A lot of gears whirled around in his head, and I heard him mumble something about ".2" and ".3" and then finally he wrote down "12.2.5". Which was great! (I then explained that by convention we only use one decimal point, so we write 12.25. And then when he said, "twelve point twenty-five," I said that made sense, but for whatever reason, we say "twelve point two five.")

Anders next asked about the square root symbol, and what it looks like on a calculator. Then he asked about the percent key, and what that's all about. So I drew a circle (which I said to imagine was a pie) and divided it into 4 pieces, and asked how much of the pie he would eat if he ate 2 pieces. (Half.) We did the same with a 6-piece pie and eating 3 pieces (half), and then a 10-piece pie and eating pieces (5 pieces would be half). Then I asked (drawing another pie but not actually dividing it into pieces) what would happen if there were 100 pieces to the pie, and he agreed 50 pieces would be half. I said that was what percent was about—that if you have something percent, that means you have something pieces out of 100. Satisfied with that answer, Anders then decided we should have a visual aid, and divided my pie into 100 pieces.

(He actually counted the lines!)

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